A GPS satellite now uses a band called link 1 (L1) having a center frequency of 1575.42 MHz and a band called link 2 (L2) having a center frequency of 1227.60 MHz. A signal from the satellite includes a code obtained by modulating a PRN (Pseudo Random Noise) code with a navigation bit as discussed later. In the present description, it is assumed that bit should mathematically take “−1” or “1”. Among the PRN codes, the code opened to civilians is a C/A code of the L1 band. The C/A code of each satellite belongs to the line of 1023 bits inherent in satellites, which is known as a gold code having a length of 1023. Each bit is often called a chip. The C/A code is transmitted at a chip rate of 1.023 MHz and repeated at one millisecond intervals. Each satellite represents data (called navigation data) required for measurement of position, such as self-position, the amount of self-clock correction and the like, as navigation bits, and 20 successive C/A codes as one unit are modulated by binary phase to be transmitted. Therefore, the navigation bits are transmitted at a bit rate of 50 bps, and the change of the navigation bits coincide with the boundary of the C/A codes.
A signal y[k] which is sent out from one GPS satellite, being discretized at a time cycle of Δt seconds, and arrives at a receiver antenna at a time t[k] (k=0, 1, 2, . . . ) is modeled as expressed by Eq. 1. In Eq. 1, “a” represents an amplitude of a received signal, pΔt second represents a time period needed to transmit the signal, b[k−p] and x[k−p] represent a value of navigation bit and a value of C/A code, respectively, when sent out, “f” represents the number of frequencies of a carrier wave and n[k] represents a noise superimposed on the received signal at the time t[k].y[k]=ab[k−p]×[k−p] cos 2πfkΔt+n[k], (k=0, 1, 2 . . . )  (1)
A receiver usually acquires a signal (baseband signal) with carrier wave components removed, by multiplying the signal by an oscillator signal, as expressed by Eq. 2.y[k]=ab[k−p]×[k−p]+n[k], (k=0, 1, 2 . . . )  (2)
The carrier wave frequency f is, however, generally different from the center frequency of the like 1 due to the Doppler shift caused by movements of the satellite and the receiver. Further, the frequency to be multiplied sometimes includes an error due to the error of an oscillator. Therefore, there may be a case where all the carrier wave components are not removed and some of them superimposes the baseband signal. In the present description, for simplification, discussion will be first made on a case where all the carrier wave components are removed.
Now considered will be a case where one of C/A codes is sampled at N KHz (N=1023×integer (≧1), where Δt=10−3/N) for one millisecond from the boundary of repetition. The sample value of C/A code has a domain which satisfies the periodic boundary condition x[k+N]=x[k] and can be extended. In this case, an autocorrelation function A[j] of the sample x[k] for one millisecond is defined as Eq. 3:
                                          A            ⁡                          [              j              ]                                =                                    1              N                        ⁢                                          ∑                                  k                  =                  0                                                  N                  -                  1                                            ⁢                                                          ⁢                                                x                  ⁡                                      [                    k                    ]                                                  ⁢                                  x                  ⁡                                      [                                          k                      -                      j                                        ]                                                                                      ,                  (                                    j              =              0                        ,                          ±              1                        ,                                          ±                2                            ⁢                                                          ⁢              …                                ⁢                                          )                                    (        3        )            
It is known that the autocorrelation function A[j] takes the maximum value of “1” when j=0 and in the neighborhood of j=0, the autocorrelation function A[j] sharply decreases and takes a very small value as compared with “1” in the range of |j|≧N/1023. Moreover, a cross-correlation function C[j] for one millisecond with respect to a C/A code x′[k] of a different satellite is expressed by Eq. 4:
                                          C            ⁡                          [              j              ]                                =                                    1              N                        ⁢                                          ∑                                  k                  =                  0                                                  N                  -                  1                                            ⁢                                                          ⁢                                                                    x                    ′                                    ⁡                                      [                    k                    ]                                                  ⁢                                  x                  ⁡                                      [                                          k                      -                      j                                        ]                                                                                      ,                  (                                    j              =              0                        ,                          ±              1                        ,                                          ±                2                            ⁢                                                          ⁢              …                                ⁢                                          )                                    (        4        )            
It is known that the cross-correlation function C[j] takes a very small value as compared with “1” with respect to arbitrary j. Theses properties largely help estimation of a signal propagation time from each GPS satellite or a pseudo range. The cross-correlation function between the received signal for one millisecond with the navigation bit not changed and the C/A code is transformed as expressed by Eq. 5:
                                                                        R                ⁡                                  [                  j                  ]                                            =                            ⁢                                                1                  N                                ⁢                                                      ∑                                          k                      =                      0                                                              N                      -                      1                                                        ⁢                                                            y                      ⁡                                              [                        k                        ]                                                              ⁢                                          x                      ⁡                                              [                                                  k                          -                          j                                                ]                                                                                                                                                                    =                            ⁢                                                                    a                    N                                    ⁢                                                            ∑                                              k                        =                        0                                                                    N                        -                        1                                                              ⁢                                                                  b                        ⁡                                                  [                                                      k                            -                            p                                                    ]                                                                    ⁢                                              x                        ⁡                                                  [                                                      k                            -                            p                                                    ]                                                                    ⁢                                              x                        ⁡                                                  [                                                      k                            -                            j                                                    ]                                                                                                                    +                                                      1                    N                                    ⁢                                                            ∑                                              k                        =                        0                                                                    N                        -                        1                                                              ⁢                                                                  n                        ⁡                                                  [                          k                          ]                                                                    ⁢                                              x                        ⁡                                                  [                                                      k                            -                            j                                                    ]                                                                                                                                                                                            =                            ⁢                                                abA                  ⁡                                      [                                          j                      -                      p                                        ]                                                  +                                                      1                    N                                    ⁢                                                            ∑                                              k                        =                        0                                                                    N                        -                        1                                                              ⁢                                                                  n                        ⁡                                                  [                          k                          ]                                                                    ⁢                                              x                        ⁡                                                  [                                                      k                            -                            j                                                    ]                                                                                                                                                                            (        5        )            
In the transformation from the second line to the third line of Eq. 5, used is a hypothesis that the navigation bit b[k−p] takes a constant value b in the range of 0≦k≦N−1. Since the first term has a sharp peak at j=p, as discussed earlier, when the signal amplitude a is sufficiently large with respect to the noise term of the second term, it is possible to estimate the signal propagation time pΔt from the GPS satellite to the receiver by detecting the peak of the cross-correlation function. If signal noise power ratio is not sufficient, however, it is impossible to discriminate the peak of the correlation function from the noise.
Though the cross-correlation function for one millisecond which corresponds to one cycle of the C/A code is used in the above case, if the navigation bit is not changed for M milliseconds which correspond to M cycles of the navigation bit, the cross-correlation function for M milliseconds can be similarly used. If the noise is independently Gaussian one, the signal noise power ratio between the peak of the first term and the noise intensity of the second term can be multiplied by M and it is therefore possible to improve the sensitivity of the receiver.
If all the carrier wave components are not removed, the peak of the autocorrelation function is impaired and the sensitivity is deteriorated. Non-Patent Document 1 is known as a method to suppress deterioration of sensitivity, where the highest peak is obtained by making a working hypothesis of possible frequency shift, correcting the frequency for the shift from the received signal and observing a cross-correlation peak. Further, as a specific example of GPS receiver, for example, a system disclosed in Patent Document 1 may be used.
In a GPS positioning system and a GPS positioning apparatus disclosed in Patent Document 1, in a process of signal processing on a received GPS signal before correlation calculation, which is called preliminary integration, the preliminary integration is performed with respect to 5 to 10 PN frames for avoiding the influence of a decrease in integral effect due to polarity reversal of the navigation data in order to achieve high sensitivity. In the phase of C/A code included in the received GPS signal, the polarity of a section phase of navigation data is reversed depending on the details of the navigation data. Therefore, since the polarity of C/A code is changed with the navigation data in such processing, when integration (cumulative addition) is performed with the polarity of C/A code, the signal components are offset and disadvantageously become not sufficient for improvement in sensitivity (S/N). In other words, the boundary of polarity reversal of the navigation data is not detected. For this reason, the number of integrals theoretically has limitations and improvement of sensitivity (S/N) is insufficient.
In a positioning process, a remote unit serving as a terminal acquires Doppler information from a base station every time, calculates a pseudo range to each visible satellite and detects a terminal position on the basis of the pseudo range or by sending the calculation result to a server. For this reason, every time when the position is measured, it is necessary to communicate with the server and this causes a problem of needing communication costs.
As another example of GPS receiving system, Patent Document 2 discloses a receiving system. In this receiving system, in order to add a peak power of cross-correlation function, regardless of any change of navigation bits, the absolute value or the square of peak power is calculated and added.
If this system is used, however, since a noise component is also added, there is a problem that the ratio of improvement in signal noise ratio relatively to an increase in the number of samples decreases.
As still another example of GPS receiver, Patent Document 3 discloses a GPS positioning system and a GPS positioning apparatus. In the GPS positioning system, however, if an incoming signal from a satellite is very weak, unless a correct navigation bit boundary can be estimated, there is a possibility that a correlation peak exceeding the noise intensity can not be obtained. In other words, there is a problem that no judgment can be made on which is the cross-correlation peak since it is buried in a noise peak.
As a system for suppressing deterioration of signal noise ratio due to the change of navigation bits, Non-Patent Document 2 discloses a system.
This system divides samples into sets by 10 milliseconds and divides the sets into two groups, one for the odd numbers (U1, U2, . . . ) and the other for the even numbers (V1, V2, . . . ). Since the change of navigation bits is caused every 20 milliseconds, the samples are included in either of the two groups. In other words, either one of a working hypothesis that no change of navigation bits is included in the group of sample sets U1, U2, . . . and another working hypothesis that no change of navigation bits is included in the group of sample sets V1, V2, . . . is true. By calculating the cross-correlation function on the premise of each working hypothesis, processing without any effect of the change of navigation bits can be performed on at least one group.
Non-Patent Document 1: written by P. Misra and P. Enge, translated by Japan Institute of Navigation, GPS Research Committee, “Global Positioning System: Signals, Measurements and Performance” (Japanese Title: “Seiei GPS”), Seiyou Bunko, 2004 (pp. 303-309, Chapter 9, Section 2, “Signal Acquisition”, especially, last paragraph of page 308)
Patent Document 1: U.S. Pat. No. 5,663,734 (FIG. 3)
Patent Document 2: National Publication of Translation No. 11-513787 (FIG. 3)
Patent Document 3: U.S. Pat. No. 3,270,407 (page 10, FIG. 1)
Non-Patent Document 2: by David M. Lin and B. Y. Tsui: “A Software GPS Receiver for Weak Signals”, IEEE Microwave Theory and Technology Society Digest, page 2139 (2001)